\subsection{Extreme case}
\subsubsection{BCS extreme}
At BCS extreme, $\mu\approx{E_{F}}$ and $\Delta\ll{}E_{F}$ and close-channel weight is small.  The largest effect is the shift of the detuning by $\mu$, which leads to larger $t_{0}(\mu)$ and larger $\Delta$. 

\subsubsection{BEC extreme}
\subsection{Tony's comment}
Tony suggested me to look into crossover experiment and see whether the BEC is made of close-channel bound state or open-channel, especially in $^{40}K$ from D. Jin.   Whether close-channel bound-state can decay? (He suspected that it was small as the coupling from close-channel bound-state to even deeper close-channel bound-state, which leads to the decay, is probably not relevant to coupling between open-close channel. )

He would like me to at least include some of the discussion of quasi-particle excitation in thesis.  